Japanese patent publication No. 2006-72829A discloses a system obtaining a blur image by using SAT (Summed-area tables).
SAT was calculated from input image data to obtain blur images. A SAT data of a pixel at (x, y) coordinates are denoted by sat(x, y). A pixel data of an input pixel is denoted by i(x, y). Then sat(x, y) is obtained as follows.
                              sat          ⁡                      (                          x              ,              y                        )                          =                              ∑                                                            x                  ′                                ≤                x                            ,                                                y                  ′                                ≤                y                                              ⁢                                          ⁢                      i            ⁡                          (                                                x                  ′                                ,                                  y                  ′                                            )                                                          [                  Equation          ⁢                                          ⁢          1                ]            
Equation 1 can be also expressed as follows:sat(x,y)=i(x,y)+sat(x−1,y)+sat(x,y−1)−sat(x−1,y−1)  [Equation 2]
sat(−1, y), sat(x, −1) and sat(−1, −1) are equal to zero at any x or y.
Following Table 1 shows an example of original data and SAT (summed area table) of a virtual image comprising 4 by 4 pixels.
TABLE 12321→ SAT Calculation →257830125811141310612161914227172328
It is necessary that SAT which has the same size of original image is calculated and then the SAT is stored in a memory to obtain blur image by using SAT as mentioned above (paragraph [0022], Japanese patent publication No. 2006-72829A). Table 1 shows an example of virtual image comprises 4 by 4 pixels. In computer systems, pixels are represented as a set of bits, usually 32 bits if a pixel represents a color. By definition, when summing 32 bits pixel values, in order to represent the full range of the result, more than 32 bits per pixels are required. In a typical case, for an image of size W times H, the required number of bits per pixels for storing the sat summation is defined as 32 bits plus four times the logarithm of W and H. For instance, for a 1280×1024 images, not less than 128 bits are required. In that sense, memory storage requirement for storing the entire SAT table may be too prohibitive in a computer graphics system. In addition, due to the number of bits per sat pixel, memory accesses may be too slow due to limited memory bandwidth. Actual images have far more pixels than the example of Table 1. Thus much memory is required to store SAT, and it takes much time to read the data from the SAT.
FIG. 1 shows the concept of SAT. In this figure, a point means a pixel of coordinates (x, y). Sat(x, y) to calculate the blur image data of the point (x, y) represented as a closed circle, is expressed as following Equation 3.
                              sat          ⁡                      (                          x              ,              y                        )                          =                                            ∑                                                                    x                    ′                                    ≤                  x                                ,                                                      y                    ′                                    ≤                  y                                                      ⁢                          i              ⁡                              (                                                      x                    ′                                    ,                                      y                    ′                                                  )                                              =                                    sat              ⁡                              (                                                      X                    r                                    ,                                      Y                    t                                                  )                                      -                          sat              ⁡                              (                                                      X                    r                                    ,                                      Y                    b                                                  )                                      -                          sat              ⁡                              (                                                      X                    l                                    ,                                      Y                    t                                                  )                                      +                          sat              ⁡                              (                                                      X                    l                                    ,                                      Y                    b                                                  )                                                                        [                  Equation          ⁢                                          ⁢          3                ]            
The blur image data of the point, which is located at the center of the coordinates (Xr, Yt), (Xr, Yb), (Xl, Yt) and (Xl, Yb) in FIG. 1, is expressed as following Equation 4. In Equation 4, w=Xr−Xl and h=Yt−Yb.
                              average          ⁡                      (                          x              ,              y                        )                          =                              sat            ⁡                          (                              x                ,                y                            )                                            w            ×            h                                              [                  Equation          ⁢                                          ⁢          4                ]            
By using SAT, it is possible to obtain any average image by adjusting w and h, which are represented as filter ratio W.
FIG. 2 shows an example of a blur image by using SAT. FIG. 2(a) shows an image when W=1 (the original image). FIG. 2(b) shows a blur image when W=5. FIG. 2(c) shows a blur image when W=15. FIG. 2(d) shows a blur image when W=30. As shown in FIG. 2, SAT enables to adjust the amount of blur effect.